The answer to this question is yes you can, but it is often quite a complex thing to understand. Insecurity hangs like a black cloud over what could be a very happy relationship.
The first question that has to be asked is whether the insecure feelings have any grounding. Does this person have any cause to feel insecurity in this relationship? In many cases they possibly do. Perhaps their partner is flirtatious by nature and shows too much attention to others. It may not automatically mean that they will be unfaithful but it can be torture for the uncertain partner.
This can cause quite reasonable feelings of insecurity and so in relationships like this then it really has to be questioned as to whether these two people are right for each other, because this will be very difficult to resolve because you are trying to change the very personality of the ‘offending’ person.
An easier insecurity to solve is where there is clearly no reason for the insecure feelings of one partner or the other. This then is certainly the perception of one individual or another that their partner is likely to stray and maybe be unfaithful. This is a common insecurity that probably has some link to a previous relationship and not the current one.
Maybe the insecure person has been cheated on at some point in the past. This kind of insecurity can even link back to a school yard incident. It’s a very powerful emotion and this is why even young adolescents can show signs of being over possessive in relationship.
One way to try and help with this kind of insecurity is to try break the link which connects it to the current relationship. It helps to talk things through, and for both partners to understand what may trigger the emotion, however this can be like walking on eggshells and it will always rear its ugly head at some point.
So if you value this relationship then a more permanent cure would be well advised otherwise it may not last.